On an inequality of S. Bernstein and estimates for the moduli of the zeros of a polynomial.

The present thesis entitled “On an inequality of S. Bernstein and estimates for the moduli of the zeros of a polynomial" is an outcome of the work carried out by author during the last two years at the Post Graduate Department of Mathematics, University of Kashmir, Srinagar. This Thesis consists of four chapters. In the first chapter, we have studied inequalities on the Maximum Modulus of a Polynomial and its Derivative. In the second chapter, we considered Lacunary type polynomials and obtain inequalities concerning the polar derivative of a polynomial. The third chapter deals with certain problems concerning a family of B operators preserving the inequalities between polynomials. Fourth chapter concerns with the location of the zeros of a polynomial with restricted coefficients.Digital copy of Ph.D thesis.University of Kashmir

Clinical profile, surgical management, outcome and follow-up of small bowel tumors.

Objectives: To study small bowel tumors with regard to 1) clinical profile; 2) Pathological classification; 3) Detection of tumors; 4) Surgical outcome; 5) Prognostic factor evaluation; & 6) Follow up. Study Design: Prospective and retrospective, hospital based. Material & Methods: a total of 40 small bowel tumors were analyzed during study period (from 1995 to 2006 onwards) – prospective/retrospective analysis. Retrospective records were collected from Department of Medical Records, SKIMS and studied. Results: Out of 40 small bowel tumors, males were 62.5%; overall mean age was 45.2 years. Most common presentation was abdominal pain (75%) followed by malena. Examination revealed abdominal mass (42.5%) as the commonest finding. Investigations carried out included CECT abdomen (60% sensitivity), CT enteroclysis (100% sensitivity), USG abdomen, EGD, barium follow and X-ray abdomen standing. Most of the tumors were malignant (82.5%); only 17.5% tumors were benign. Most common malignant tumor was adenocarcinoma (57.5%) whereas most common benign tumor was leiomyoma (5/7, 71%). Most common site was ileum (50%), for benign as well as malignant tumors. Metastasis and curative resection were prognostic factors. Mean survival was 51 months; overall survival rate was 55% and overall censored rate was 45%. Conclusions: Small bowel tumors are rare. Incidence is 0.2% of all gastrointestinal tumors; 0.1% of all surgical malignancies. Metastasis, surgical resection and type of tumor are prognostic factors